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Inequalities - Intermediate Level: mathematical inequalities INTERMEDIATE

Comprehensive weakness targeting worksheet covering 20 intermediate-level inequalities problems. Worksheet 18 of 30 emphasizes mathematical inequalities. Master symbolic inequalities, chain inequalities, inequality solving through detailed explanations. Difficulty: moderate complexity with mixed patterns. Tailored for mid-level preparation.

📝 Worksheet 18 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Intermediate level

What you'll learn in this worksheet:
Your progress through Inequalities
Worksheet 18 of 30 (60% complete)

Question 1

Directions: @ means >, # means <, & means =, % means ≤, $ means ≥ Statement: P & Q % S # U Which conclusion follows?
Decoding: P = Q → = Q ≤ S → ≤ S < U. Therefore, No definite conclusion.
coded, symbols, decoding

Question 2

Arrange the elements B, A, D, E, C based on these clues: - B > A - D > E - E > C - D < A Which element is the largest?
From the clues: B > A > D > E > C. Therefore, B is the largest.
puzzle, arrangement, ordering

Question 3

Statements: I. B ≥ F > A II. A < E ≤ D Which conclusion is definitely false?
From the statements, B < D contradicts the established relationships and is definitely false.
reverse, mixed, direction

Question 4

Statements: I. C ≥ B > D II. D < A ≤ F Which conclusion is definitely false?
From the statements, C < F contradicts the established relationships and is definitely false.
reverse, mixed, direction

Question 5

Statements: I. A < E > C II. E ≤ B < D Which conclusion is definitely false?
From the statements, A > D contradicts the established relationships and is definitely false.
reverse, mixed, direction

Question 6

Statements: I. E < A > F II. A ≤ B < D Which conclusion is definitely false?
From the statements, E > D contradicts the established relationships and is definitely false.
reverse, mixed, direction

Question 7

Directions: ! means >, ~ means =, ? means <, ^ means ≤, * means ≥ Statement: Q * U ~ R ! P Which conclusion follows?
Decoding: Q ≥ U → ≥ U = R → = R > P. Therefore, No definite conclusion.
coded, symbols, decoding

Question 8

Statements: G ≥ A ≥ H > F Conclusion: F > G Is the conclusion true?
From G ≥ A ≥ H > F, F > G contradicts the given inequalities, so it's false.
basic, comparison, transitive

Question 9

Statements: T > Q; Q > S; Q > P; S = U; P ≥ V Which of the following is definitely true?
Analyzing the chain: T > Q; Q > S; Q > P; S = U; P ≥ V. Therefore, T > S is definitely true.
complex, chain, multi-step

Question 10

Statements: T > R ≥ S; P ≤ S < V; V = Q; Q ≥ U Which of the following is definitely true?
Analyzing the chain: T > R ≥ S; P ≤ S < V; V = Q; Q ≥ U. Therefore, S < Q is definitely true.
complex, chain, multi-step

Question 11

Statements: T > S; S > U; S > V; U = R; V ≥ W Which of the following is definitely true?
Analyzing the chain: T > S; S > U; S > V; U = R; V ≥ W. Therefore, T > V is definitely true.
complex, chain, multi-step

Question 12

Statement: X ≤ W ≤ Y Conclusions: I. X < Y II. X = Y Which follows?
From X ≤ W ≤ Y, either X < Y or X = Y. Hence either I or II follows.
either-or, logical, possibility

Question 13

Arrange the elements C, A, D, B, E based on these clues: - D < A - D > B - C > A - B > E Which element is the largest?
From the clues: C > A > D > B > E. Therefore, C is the largest.
puzzle, arrangement, ordering

Question 14

Statements: C ≥ A = E ≥ F Conclusion: C ≥ F Is the conclusion true?
From C ≥ A = E ≥ F, using transitivity, C ≥ F is definitely true.
basic, comparison, transitive

Question 15

Statements: I. D ≥ F = E II. E > A ≥ G Which conclusions definitely follow?
Combining statements: D ≥ F = E > A ≥ G. Therefore, I, II, and III definitely follow(s).
compound, multiple, chain

Question 16

Statement: V > Y > W Conclusions: I. V > W II. V < W Which follows?
From V > Y > W, V > W is definitely true. II does not follow.
either-or, logical, possibility

Question 17

Arrange the elements C, B, A, D, E based on these clues: - A > D - D > E - A < B - C > B Which element is the largest?
From the clues: C > B > A > D > E. Therefore, C is the largest.
puzzle, arrangement, ordering

Question 18

Statements: B ≥ A ≥ F ≥ C Conclusion: A = C Is the conclusion true?
From B ≥ A ≥ F ≥ C, we cannot determine the exact relationship between A and C.
basic, comparison, transitive

Question 19

Statement: Z ≤ V ≤ Y Conclusions: I. Z < Y II. Z = Y Which follows?
From Z ≤ V ≤ Y, either Z < Y or Z = Y. Hence either I or II follows.
either-or, logical, possibility

Question 20

Statement: N = R > S ≥ Q > M Which conclusions are definitely true?
From N = R > S ≥ Q > M, we can derive: R > Q, S > M. These conclusions definitely follow.
multiple, evaluation, analysis
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